Question

Which of the following points is a solution of the inequality y < -|x|?

Answer 1

Answer: choice A only

(1,-2) is the only solution (from the list of choices)

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Explanation:

Let's go through each answer choice. We'll plug the coordinates in one at a time.

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Choice A has the point (1,-2) so x = 1 and y = -2 pair up together

y < -|x|

-2 < -|1|

-2 < -1

This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.

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Choice B) plug in (x,y) = (1,-1)

y < -|x|

-1 < -|1|

-1 < -1

False. A number is not smaller than itself. So we can cross B off the list.

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Choice C) plug in (x,y) = (1,0)

y < -|x|

0 < -|1|

0 < -1

This is false because -1 is smaller than 0. Cross choice C off the list.

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Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.

The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.

Answer 2

C because it is an inequality